Preheat oven to 350°F (175°C). Grease an 8x8-inch cake pan and line with parchment paper.
Make the Streusel: Mix brown sugar, flour, and cinnamon in a bowl. Cut in cold butter until crumbly. Refrigerate until ready to use.
Prepare the Cake Batter: In a bowl, whisk together gluten-free flour, baking powder, baking soda, and salt.
In a separate bowl, beat butter and sugar until light and fluffy. Add eggs, vanilla, and sour cream, mixing well.
Gradually mix in the dry ingredients, alternating with milk. Do not overmix.
Assemble the Cake: Pour half the batter into the cake pan. Sprinkle half the streusel topping evenly. Add the remaining batter and top with the rest of the streusel.
Bake for 32-38 minutes, or until a toothpick comes out clean.
Let the cake cool in the pan for 15 minutes before serving.